After a ton of trouble finding a laser cutter shop that would actually cut the plywood for me, I managed to complete the fabrication in the University machine shop using their 60W Epilog laser cutter. Settings were as follows:

Please keep an eye on the cutting incase there's any fire. My suggestion is that you arrange all of the designs onto a single 12"x24" canvas first before you do the first cut. I made the mistake of not doing so and ended up wasting a lot of space on one of the sheets. 

Here's more data on setting kerf values which I wish I found before the fabrication: http://www.cutlasercut.com/resources/tips-and-advice/what-is-laser-kerf and here's the calibration method: https://www.instructables.com/id/How-to-Adjust-for-Wood-Thickness-and-Kerf-on-a-Las/